Geodesic
Free curves on varieties
Documenta mathematica, Tome 21 (2016), pp. 287-308.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study various generalisations of rationally connected varieties, allowing the connecting curves to be of higher genus. The main focus will be on free curves $f:C\to X$ with large unobstructed deformation space as originally defined by Kollár, but we also give definitions and basic properties of varieties $X$ covered by a family of curves of a fixed genus $g$ so that through any two general points of $X$ there passes the image of a curve in the family. We prove that the existence of a free curve of genus $g\geq1$ implies the variety is rationally connected in characteristic zero and initiate a study of the problem in positive characteristic.
Classification : 14M20, 14M22, 14H10 
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     author = {Gounelas, Frank},
     title = {Free curves on varieties},
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     pages = {287--308},
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     volume = {21},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a34/}
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Gounelas, Frank. Free curves on varieties. Documenta mathematica, Tome 21 (2016), pp. 287-308. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a34/